More precisely, the invention relates to a method whereby the flow of fluid produced by the well is modified by closing or opening a valve located on the surface or in the well. The resulting pressure variations are measured or recorded down-hole or on the surface as a function of the time elapsing since the beginning of the tests, i.e. since the flow modification. The characteristics of the well-subsurface formation system can be deduced from these experimental data. They are analyzed by comparing the response of the subsurface formation to a change in the flow of fluid produced, with the behavior of theoretical models having well-defined characteristics and subjected to the same flow change as the investigated formation. Usually, the pressure variations as a function of time characterize the behavior of the well-formation system, and the removal of fluids at constant flow, by opening an initially closed valve in the well, is the test condition which is applied to the formation and to the theoretical model. When their behaviors are identical, it is assumed that the investigated system and theoretical model are identical from the quantitative as well as the qualitative viewpoints. In other words, these reservoirs are assumed to have the same physical characteristics.
The characteristics obtained from this comparison depend on the theoretical model: the more complicated the model, the greater the number of characteristics which can be determined. The basic model is represented by a homogeneous formation with impermeable upper and lower limits and with an infinite radial extension. The flow in the formation is then radial, directed toward the well. However, the theoretical model most currently used is more complicated. It comprises the characteristics of the basic model to which are added internal conditions such as the skin effect and the wellbore storage effect. The skin effect is defined by a coefficient S which characterizes the damage or the stimulation of the part of the formation adjacent to the well. The wellbore storage effect is characterized by a coefficient C which results from the difference in the flow of fluid produced by the well between the subsurface formation and the wellhead when a valve located at the wellhead is either closed or opened. The coefficient C is usually expressed in barrels per psi, a barrel being equal to 0.16 m.sup.3 and a psi to 0.069 bar.
The behavior of a theoretical model is represented conveniently by a network of typical curves which represent the down-hole fluid pressure variations as a function of time. These curves are usually plotted in cartesian coordinates and in a logarithmic scale, the dimensionless pressure being plotted on the ordinate and the dimensionless time on the abscissa. In addition, each curve is characterized by one or more dimensionless numbers, each representing a characteristic (or a combination of characteristics) of the theoretical system formed by a well and a reservoir. A dimensionless parameter is defined by the real parameter (pressure for example) multiplied by an expression which includes certain characteristics of the well-reservoir system so as to make the dimensionless parameter independent of these characteristics. Thus, the coefficient S characterizes only the skin effect but is independent of the other characteristics of the reservoir and of the experimental conditions such as flow rate, viscosity of fluid, permeability of formation, etc. When the theoretical model and the investigated well-formation system correspond, the experimental curve and one of the type curves represented with the same scales of coordinates have the same form but are offset in relation to each other. The offsets along the two axes, on the ordinate for pressure and on the abscissa for time, are proportional to values of characteristics of the well-reservoir system which can thus be determined.
Qualitative information on the subsurface formation, such as the presence of a fracture for example, is obtained by identifying the different flows on the network in logarithmic scale representing the experimental data. Knowing that a particular characteristic of the well-reservoir system, a vertical fracture for example, is characterized by particular flow conditions, all the different flows appearing in the graph of the experimental data are identified to select the appropriate well-reservoir system model. The characteristics of the formation are obtained by selecting a typical curve having the same form as the experimental curve and determining the offset of the axes of the coordinates of the experimental curve in relation to the theoretical curve.
Several networks of typical curves correspond to a given theoretical model. This depends on the dimensionless parameters chosen for representing the axes of coordinates, as well as on one or more indexes. An index is nothing other than an additional parameter (or combination of parameters) chosen to represent the curves, in addition to the dimensionless parameters of the axes of coordinates.
A comparison of the different methods used is given in the article entitled "A Comparison Between Different Skin and Wellbore Storage Type Curves for Early-Time Transient Analysis" by A. C. Gringarten & al., published by the "Society of Petroleum Engineers of AIME", (No. SPE 8205). The U.S. Pat. No. 4,328,705 also describes a method according to which the type curves are represented using the dimensionless pressure P.sub.D for the access of ordinates and the ratio t.sub.D /C.sub.D for the access of abscissas, t.sub.D being the dimensionless time and C.sub.D the dimensionless coefficient characterizing the wellbore storage effect. The drawback of the method described in that patent is that the type curves have shapes varying relatively slowly with respect to each other. This results in some uncertainty in the choice of type curves corresponding to the experimental curve. It is also noted that, for a complete analysis, one is required to use not only a graph in logarithmic scale representing all the experimental data, but also specialized graphs in semi-logarithmic scale for example, to analyze only part of the data but in a more precise manner.
A procedure has already been tried whereby the mathematical derivative of the dimensionless pressure P'.sub.D' is used instead of the dimensionless pressure P.sub.D. According to Bourdet et al, U.S. Pat. No. 4,597,290, issued July 1, 1986 and the article "A New Set of Type Curves Simplifies Well Test Analysis" published in the May 1983 issue of World Oil, the curve of the derivative .DELTA.P' of the experimentally measured pressure is plotted and this curve is matched with a type curve of a typical network P'.sub.D (t.sub.D /C.sub.D).
Such a method gives satisfactory results but requires pressure measurements in the well over a relatively long period.
It is the object of the present invention to provide a new method making it possible to shorten the experimental time in the field. This method makes advantageous use of the derivative P'.sub.D of the dimensionless pressure. It is moreover based upon Green's functions (see Carslaw H. S. and Jaeger J. C., "Conduction of Heat in Solids", Second Edition, Oxford University Press, 1959) which relate to the analysis of pressure transients. Briefly, Green's functions provide the pressure variations with respect to time created by a source (or a well--in the fluid mechanics sense) of instantaneous action and unit intensity (Dirac pulse, i.e. a pulse with a duration of .DELTA.t and an amplitude of 1/.DELTA.t, the surface of the pulse being equal to 1, and .DELTA.t tending towards zero). Mathematically, Green's functions correspond to the derivatives with respect to time of the type curves P.sub.D used as a theoretical model. The result is that if a formation is subjected to an instantaneous action of unit intensity, the curve of subsequent pressure variations may be matched with a suitable curve P'.sub.D.
In practice, it is not possible to subject the formation to an instantaneous action of unit intensity, as the injection or production of fluid corresponding to this action must necessarily last a finite time. However, the experiment demonstrated that the action could extend over a few minutes without any detriment to the quality of the results.